The present invention relates to a frequency response function measuring method for obtaining a frequency response function matrix of a multi-input/multi-output object by applying thereto waveforms from a plurality of waveform generators and multiplying its input-output cross spectral matrix by an inverse matrix of its input auto spectral matrix.
Multi-point excitation is needed for measuring the frequency response function of a structure which cannot be sufficiently excited by one-point excitation, that is, an excitation applied as a vibrating force to a single point on an object. With one-point excitation, a modal parameter of the characteristic frequency varies with the point of excitation. With multi-point excitation, however, the modal parameter is less dispersive because the entire structure can be excited with a constant exciting force, and measured frequency response functions are less inconsistent among them because a plurality of frequency response functions are measured at the same time.
An output spectrum S.sub.y (i) at a point i is expressed by a linear combination of a conditional frequency response function L(i, j) between each excitation point j and the output point i with an input spectrum S.sub.x (j) at the excitation point j, as follows: EQU S.sub.y (i)=L(i, 1)S.sub.x (1)+L(i, 2)S.sub.x (2)+ (1)
Accordingly, a multi-input model is essentially a matrix and a frequency response function matrix (L) is a transformation of an input-output cross spectral matrix [G.sub.yx ] from an input auto spectral matrix [G.sub.xx ]; namely, EQU [G.sub.yx ]=[L][G.sub.xx ] (2)
A conditional frequency response function matrix to be obtained is given as follows: EQU L]=[G.sub.yx ][G.sub.xx ].sup.-1 ( 3)
This equation holds irrespective of whether exciting forces are correlated to one another or not.
The prior art employs, for the multi-point excitation, signals which are not correlated in their exciting force. In the case of using pure random signals for excitation, however, since a Fourier transformation is performed after multiplying the response waveform by a window function, a leakage error occurs. This results in the gain being measured rather small for a resonant structure with a sharp frequency response function; therefore, the attenuation factor is overestimated.
There has been proposed a burst random excitation method in which pure random waves are generated repeatedly in a burst-like manner for a period of time 1/2 to 2/3 of an analysis frame. With this method, in the case of a response with a small attenuation factor, it is necessary to multiply the response waveform by an attenuation term so that an attenuation occurs in the analysis frame. However, this may sometimes affect the frequency resolution, the gain and an estimate of the phase of the conditional frequency response function. Conversely, in the case of a response with a large attenuation factor, a free response after the duration of the burst wave is observed in the analysis frame. This causes correlation among output signals or conditional output signals and decreases independent information of the input-output cross spectral matrix [G.sub.yx ] of Eq. (2), introducing the possibility of making it impossible to measure the conditional frequency response function.